Atkin-Lehner |
2+ 3- 5- 17+ |
Signs for the Atkin-Lehner involutions |
Class |
48960cv |
Isogeny class |
Conductor |
48960 |
Conductor |
∏ cp |
2 |
Product of Tamagawa factors cp |
deg |
12288 |
Modular degree for the optimal curve |
Δ |
-190356480 = -1 · 210 · 37 · 5 · 17 |
Discriminant |
Eigenvalues |
2+ 3- 5- -3 -3 -4 17+ 1 |
Hecke eigenvalues for primes up to 20 |
Equation |
[0,0,0,-12,664] |
[a1,a2,a3,a4,a6] |
Generators |
[5:27:1] |
Generators of the group modulo torsion |
j |
-256/255 |
j-invariant |
L |
4.5711700712971 |
L(r)(E,1)/r! |
Ω |
1.4472587638054 |
Real period |
R |
1.5792511282645 |
Regulator |
r |
1 |
Rank of the group of rational points |
S |
1.000000000008 |
(Analytic) order of Ш |
t |
1 |
Number of elements in the torsion subgroup |
Twists |
48960fk1 6120t1 16320bd1 |
Quadratic twists by: -4 8 -3 |